Question

The velocity of a body at time t = 0 is $10\sqrt{2}$ m/s in the north-east direction and it is moving with an acceleration of 2 m/s² directed towards the south. The magnitude and direction of the velocity of the body after 5 sec will be

• A. 10 m/s, towards east
• B. 10 m/s, towards north
• C. 10 m/s, towards south
• D. 10 m/s, towards north-east

Answer 1

Answer: (A)

10 m/s, towards east

Answer 2

$\overset{\rightarrow}{v} = \overset{\rightarrow}{u} + \overset{\rightarrow}{a}t$ ∴ $v = \sqrt{u^{2} + a^{2}t^{2} + 2uat\cos\theta}$

$v = \sqrt{200 + 100 + 2 \times 10\sqrt{2} \times 10 \times \cos 135} = 10m/s$

$\tan\alpha = \frac{at\sin\theta}{u + at\cos\theta}\frac{10\sin 135}{10\sqrt{2} + 10\cos 135} = 1$

∴$\alpha = 45{^\circ}$

i.e. resultant velocity is 10 m/s towards East.